请贵团帮忙解决一下这道大学概率论与数理统计题目 感激不尽!

U=0。5(X-Y)X=Z+UY=Z-U|jacob|=det{(dx/dz dy/dz),(dx/du dy/du) }=|-2|=2f(u,z)=f(x,y)|jacob|=2/{(x^2+1)(y^2+1)} (1/π^2)=(2/π^2)((z+u)^2+1)((z-u)^2+1)fz(z)=∫(实数全域) f(u,z) du[ln{(u^2+2uz+z^2+1)/(u^2-2zu+z^2+1)}+2zarctan(u+z)+2zarctan(u-z)]/{z(4z^2+4)π^2} |u~(-无穷~无穷))=(ln(1)-ln(1)+2zπ+2zπ)/{4z(z2+1)π^2}=4π/4π^2(z^2+1)fz(z)=1/{π(z^2+1)}那块积分用设系数大法,把它拆成(Au+B)/((u+z)^2+1)+(Cu+D)/((-u+z)^2+1)之后分成积分符合自然对数和反正切的部分